Standard form of a line that has a slope of -1 and passes through (-5,-1)

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?

vichka [17]

Answer:

$x = 5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}$

Step-by-step explanation:

We need to solve the quadratic equation

6 = x^2 -10x

Rearranging we get,

x^2-10x-6=0

Using quadratic formula to solve the quadratic equation

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a= 1, b =-10 and c=6

Putting values in the quadratic formula

$x=\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(-6)}}{2(1)}\\x=\frac{10\pm\sqrt{100+24}}{2}\\x=\frac{10\pm\sqrt{124}}{2}\\x=\frac{10\pm\sqrt{2*2*31}}{2}\\x=\frac{10\pm\sqrt{2^2*31}}{2}\\x=\frac{10\pm2\sqrt{31}}{2}\\x = 5\pm\sqrt{31}$

So, $x=5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}$

3 0

3 years ago

Read 2 more answers

What is the slope of a line perpendicular to the line whose equation is 3x+6y=-183x+6y=−18. Fully reduce your answer.

schepotkina [342]

Answer:

2

Step-by-step explanation:

The given equation of line is

$3x+6y=-18$

We need to find the slope of a line which is perpendicular to the given line.

The given equation can be rewritten as

$3x+6y+18=0$ ...(i)

If a line is defined as $ax+bx+c=0$ , then the slope of the line is

$m=-\dfrac{a}{b}$

In equation (i), a=3, b=6 and c=18. So, slope of the line is

$m_1=-\dfrac{3}{6}=-\dfrac{1}{2}$

Let $m_2$ be the slope of perpendicular line.

We know that product of two perpendicular line is -1.

$m_1\cdot m_2=-1$

$(-\dfrac{1}{2})\cdot m_2=-1$

Multiply both sides by -2.

$m_2=2$

Therefore, the slope of perpendicular line is 2.

6 0

3 years ago

What is 2+x if x=2? thanks

11Alexandr11 [23.1K]

Reorder 2 and x.
x + 2

4 0

3 years ago

Read 2 more answers

Help if u can! don't answer if u don't know please

lara31 [8.8K]

By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

<h3>What is a function?</h3>

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

<h3>The types of function.</h3>

In Mathematics, there are different types of functions and these include the following;

Periodic function

Inverse function

Modulus function

Signum function

Piece-wise defined function.

Logarithm function

<h3>What is a logarithm function?</h3>

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.

Therefore, if log₁₀x < 1, then, x < 10. Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

The upper left number can't be smaller than 1 but its log must be the smallest. Thus, if the exponent equals 0, the red box can assume any number.

The fractions in the lower left and upper right should be as large as possible with their denominators being small while their numerators are large.

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

Read more on logarithm function here: brainly.com/question/26788007

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